Sparse Representations and Compressive Sensing for Imaging and Vision

Sparse Representations and Compressive Sensing for Imaging and Vision
Author: Vishal M. Patel
Publisher: Springer Science & Business Media
Total Pages: 111
Release: 2013-02-11
Genre: Technology & Engineering
ISBN: 1461463815
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Compressed sensing or compressive sensing is a new concept in signal processing where one measures a small number of non-adaptive linear combinations of the signal. These measurements are usually much smaller than the number of samples that define the signal. From these small numbers of measurements, the signal is then reconstructed by non-linear procedure. Compressed sensing has recently emerged as a powerful tool for efficiently processing data in non-traditional ways. In this book, we highlight some of the key mathematical insights underlying sparse representation and compressed sensing and illustrate the role of these theories in classical vision, imaging and biometrics problems.

Sparse and Redundant Representations

Sparse and Redundant Representations
Author: Michael Elad
Publisher: Springer Science & Business Media
Total Pages: 376
Release: 2010-08-12
Genre: Mathematics
ISBN: 1441970118
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A long long time ago, echoing philosophical and aesthetic principles that existed since antiquity, William of Ockham enounced the principle of parsimony, better known today as Ockham’s razor: “Entities should not be multiplied without neces sity. ” This principle enabled scientists to select the ”best” physical laws and theories to explain the workings of the Universe and continued to guide scienti?c research, leadingtobeautifulresultsliketheminimaldescriptionlength approachtostatistical inference and the related Kolmogorov complexity approach to pattern recognition. However, notions of complexity and description length are subjective concepts anddependonthelanguage“spoken”whenpresentingideasandresults. The?eldof sparse representations, that recently underwent a Big Bang like expansion, explic itly deals with the Yin Yang interplay between the parsimony of descriptions and the “language” or “dictionary” used in them, and it became an extremely exciting area of investigation. It already yielded a rich crop of mathematically pleasing, deep and beautiful results that quickly translated into a wealth of practical engineering applications. You are holding in your hands the ?rst guide book to Sparseland, and I am sure you’ll ?nd in it both familiar and new landscapes to see and admire, as well as ex cellent pointers that will help you ?nd further valuable treasures. Enjoy the journey to Sparseland! Haifa, Israel, December 2009 Alfred M. Bruckstein vii Preface This book was originally written to serve as the material for an advanced one semester (fourteen 2 hour lectures) graduate course for engineering students at the Technion, Israel.

Sparse representation of visual data for compression and compressed sensing

Sparse representation of visual data for compression and compressed sensing
Author: Ehsan Miandji
Publisher: Linköping University Electronic Press
Total Pages: 158
Release: 2018-11-23
Genre:
ISBN: 9176851869
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The ongoing advances in computational photography have introduced a range of new imaging techniques for capturing multidimensional visual data such as light fields, BRDFs, BTFs, and more. A key challenge inherent to such imaging techniques is the large amount of high dimensional visual data that is produced, often requiring GBs, or even TBs, of storage. Moreover, the utilization of these datasets in real time applications poses many difficulties due to the large memory footprint. Furthermore, the acquisition of large-scale visual data is very challenging and expensive in most cases. This thesis makes several contributions with regards to acquisition, compression, and real time rendering of high dimensional visual data in computer graphics and imaging applications. Contributions of this thesis reside on the strong foundation of sparse representations. Numerous applications are presented that utilize sparse representations for compression and compressed sensing of visual data. Specifically, we present a single sensor light field camera design, a compressive rendering method, a real time precomputed photorealistic rendering technique, light field (video) compression and real time rendering, compressive BRDF capture, and more. Another key contribution of this thesis is a general framework for compression and compressed sensing of visual data, regardless of the dimensionality. As a result, any type of discrete visual data with arbitrary dimensionality can be captured, compressed, and rendered in real time. This thesis makes two theoretical contributions. In particular, uniqueness conditions for recovering a sparse signal under an ensemble of multidimensional dictionaries is presented. The theoretical results discussed here are useful for designing efficient capturing devices for multidimensional visual data. Moreover, we derive the probability of successful recovery of a noisy sparse signal using OMP, one of the most widely used algorithms for solving compressed sensing problems.

Compressed Sensing

Compressed Sensing
Author: Yonina C. Eldar
Publisher: Cambridge University Press
Total Pages: 557
Release: 2012-05-17
Genre: Technology & Engineering
ISBN: 1107394392
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Compressed sensing is an exciting, rapidly growing field, attracting considerable attention in electrical engineering, applied mathematics, statistics and computer science. This book provides the first detailed introduction to the subject, highlighting theoretical advances and a range of applications, as well as outlining numerous remaining research challenges. After a thorough review of the basic theory, many cutting-edge techniques are presented, including advanced signal modeling, sub-Nyquist sampling of analog signals, non-asymptotic analysis of random matrices, adaptive sensing, greedy algorithms and use of graphical models. All chapters are written by leading researchers in the field, and consistent style and notation are utilized throughout. Key background information and clear definitions make this an ideal resource for researchers, graduate students and practitioners wanting to join this exciting research area. It can also serve as a supplementary textbook for courses on computer vision, coding theory, signal processing, image processing and algorithms for efficient data processing.

Handbook of Mathematical Methods in Imaging

Handbook of Mathematical Methods in Imaging
Author: Otmar Scherzer
Publisher: Springer Science & Business Media
Total Pages: 1626
Release: 2010-11-23
Genre: Mathematics
ISBN: 0387929193
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The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.

Sparse Representations for Radar with MATLAB Examples

Sparse Representations for Radar with MATLAB Examples
Author: Peter Knee
Publisher: Springer Nature
Total Pages: 71
Release: 2022-05-31
Genre: Technology & Engineering
ISBN: 3031015193
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Although the field of sparse representations is relatively new, research activities in academic and industrial research labs are already producing encouraging results. The sparse signal or parameter model motivated several researchers and practitioners to explore high complexity/wide bandwidth applications such as Digital TV, MRI processing, and certain defense applications. The potential signal processing advancements in this area may influence radar technologies. This book presents the basic mathematical concepts along with a number of useful MATLAB® examples to emphasize the practical implementations both inside and outside the radar field. Table of Contents: Radar Systems: A Signal Processing Perspective / Introduction to Sparse Representations / Dimensionality Reduction / Radar Signal Processing Fundamentals / Sparse Representations in Radar

A Wavelet Tour of Signal Processing

A Wavelet Tour of Signal Processing
Author: Stephane Mallat
Publisher: Elsevier
Total Pages: 663
Release: 1999-09-14
Genre: Computers
ISBN: 0080520839
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This book is intended to serve as an invaluable reference for anyone concerned with the application of wavelets to signal processing. It has evolved from material used to teach "wavelet signal processing" courses in electrical engineering departments at Massachusetts Institute of Technology and Tel Aviv University, as well as applied mathematics departments at the Courant Institute of New York University and École Polytechnique in Paris. Provides a broad perspective on the principles and applications of transient signal processing with wavelets Emphasizes intuitive understanding, while providing the mathematical foundations and description of fast algorithms Numerous examples of real applications to noise removal, deconvolution, audio and image compression, singularity and edge detection, multifractal analysis, and time-varying frequency measurements Algorithms and numerical examples are implemented in Wavelab, which is a Matlab toolbox freely available over the Internet Content is accessible on several level of complexity, depending on the individual reader's needs New to the Second Edition Optical flow calculation and video compression algorithms Image models with bounded variation functions Bayes and Minimax theories for signal estimation 200 pages rewritten and most illustrations redrawn More problems and topics for a graduate course in wavelet signal processing, in engineering and applied mathematics

Compressed Sensing & Sparse Filtering

Compressed Sensing & Sparse Filtering
Author: Avishy Y. Carmi
Publisher: Springer Science & Business Media
Total Pages: 505
Release: 2013-09-13
Genre: Technology & Engineering
ISBN: 364238398X
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This book is aimed at presenting concepts, methods and algorithms ableto cope with undersampled and limited data. One such trend that recently gained popularity and to some extent revolutionised signal processing is compressed sensing. Compressed sensing builds upon the observation that many signals in nature are nearly sparse (or compressible, as they are normally referred to) in some domain, and consequently they can be reconstructed to within high accuracy from far fewer observations than traditionally held to be necessary. Apart from compressed sensing this book contains other related approaches. Each methodology has its own formalities for dealing with such problems. As an example, in the Bayesian approach, sparseness promoting priors such as Laplace and Cauchy are normally used for penalising improbable model variables, thus promoting low complexity solutions. Compressed sensing techniques and homotopy-type solutions, such as the LASSO, utilise l1-norm penalties for obtaining sparse solutions using fewer observations than conventionally needed. The book emphasizes on the role of sparsity as a machinery for promoting low complexity representations and likewise its connections to variable selection and dimensionality reduction in various engineering problems. This book is intended for researchers, academics and practitioners with interest in various aspects and applications of sparse signal processing.

Compressive Sensing for Computer Vision and Image Processing

Compressive Sensing for Computer Vision and Image Processing
Author: Naveen Kulkarni
Publisher:
Total Pages: 84
Release: 2011
Genre: Computer vision
ISBN:
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With the introduction of compressed sensing and sparse representation, many image processing and computer vision problems have been looked at in a new way. Recent trends indicate that many challenging computer vision and image processing problems are being solved using compressive sensing and sparse representation algorithms. This thesis assays some applications of compressive sensing and sparse representation with regards to image enhancement, restoration and classication. The first application deals with image Super-Resolution through compressive sensing based sparse representation. A novel framework is developed for understanding and analyzing some of the implications of compressive sensing in reconstruction and recovery of an image through raw-sampled and trained dictionaries. Properties of the projection operator and the dictionary are examined and the corresponding results presented. In the second application a novel technique for representing image classes uniquely in a high-dimensional space for image classification is presented. In this method, design and implementation strategy of the image classification system through unique affine sparse codes is presented, which leads to state of the art results. This further leads to analysis of some of the properties attributed to these unique sparse codes. In addition to obtaining these codes, a strong classier is designed and implemented to boost the results obtained. Evaluation with publicly available datasets shows that the proposed method outperforms other state of the art results in image classication. The final part of the thesis deals with image denoising with a novel approach towards obtaining high quality denoised image patches using only a single image. A new technique is proposed to obtain highly correlated image patches through sparse representation, which are then subjected to matrix completion to obtain high quality image patches. Experiments suggest that there may exist a structure within a noisy image which can be exploited for denoising through a low-rank constraint.